Apollo
VIP
There is no proof that Cushites themselves migrated to South Africa, only that the San Bushman have Cushitic admixture.
They most likely intermingled in Kenya/Tanzania, which is where the Southern Cushites(who also have Khoisan admixture) live.
Nope.
That African archaeogenetic study had samples of extinct lake Malawi hunter-gatherers and they were not the variety the South Cushites mixed with to create the proto-Khoi/Nama. Near-full blood South Cushites mixed with far Southern San-type (''true Khoisan''). Not the semi-Khoisans found in Southeast Africa, but the Chinaman looking ones from the Kalahari.
So South Cushites made it to the area around Namibia/Botswana/Southwest South Africa. The edge of Southern Africa.